What are the divisors of 6180?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 103, 206, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 3090, 6180

There is a total of 24 positive divisors.
The sum of these divisors is 17472.
The arithmetic mean is 728.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 206, 412, 618, 1030, 1236, 2060, 3090, 6180

8 odd divisors

1, 3, 5, 15, 103, 309, 515, 1545

How to compute the divisors of 6180?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 6180 by each of the numbers from 1 to 6180 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

6180 / 1 = 6180 (the remainder is 0, so 1 is a divisor of 6180)
6180 / 2 = 3090 (the remainder is 0, so 2 is a divisor of 6180)
6180 / 3 = 2060 (the remainder is 0, so 3 is a divisor of 6180)
...
6180 / 6179 = 1.0001618384852 (the remainder is 1, so 6179 is not a divisor of 6180)
6180 / 6180 = 1 (the remainder is 0, so 6180 is a divisor of 6180)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 6180 (i.e. 78.612976028134). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

6180 / 1 = 6180 (the remainder is 0, so 1 and 6180 are divisors of 6180)
6180 / 2 = 3090 (the remainder is 0, so 2 and 3090 are divisors of 6180)
6180 / 3 = 2060 (the remainder is 0, so 3 and 2060 are divisors of 6180)
...
6180 / 77 = 80.25974025974 (the remainder is 20, so 77 is not a divisor of 6180)
6180 / 78 = 79.230769230769 (the remainder is 18, so 78 is not a divisor of 6180)